Current solutions for beamforming and spatial filtering work best for static geometrical arrangements in which the speaker's position doesn't move much relative to the position of the microphones. Adaptive filters can track the speaker but they need time to converge. Accordingly, during the time directly after movements of the speaker or of the device performance may be degraded.
Another class of systems tries to estimate the ratio of coherent sound energy (generally as desired component) and diffuse sound energy (generally interference). The CDR may be used directly to calculate a filter for noise reduction.